You might find one of the A8 or A10 mobile APU's with a 35-45tdp rating that can probably get the job done using the flgrx proprietary driver in gentoo stable or the radeonsi driver in unstable. In the former case, I find that using the open drivers reveals a bug in xorg that causes X to hang on event processing. That appears to be fixed in the unstable version, but there's still "grunge" with display artifacts that need to be wrung out. Glamor and GLES don't seem to get along with each other yet.

I do have an A10 7850 in a mythtv setup, but it's in a traditional minitower with the stock fan based cooler. It is quiet enough for me though.

Now I dont know for sure how good the driver and decoding support is on those GPU's under linux atm. Intel seems to have linux drivers and from what I read there should be opensoruce drivers to. But you have to do some research in to that but they have the hardware needed and I think intel is working on drivers pretty hard for bay trail. I just dont have any interest in drivers for that board my self

Any way I run that passively. CPU runs at 53C idle. About 60C full load on all cores.
The chassis do need vent holes for the hot air to get out.
It compiles my Linux kernel in 8 minutes and benchmarks 8.8GFLOPS so its pretty fast for more common tasks but its not a number cruncher. My i7 3930K @ 4Ghz compiles a kernel in just under 1 minute so yea 8min for 10W SoC is dam good. Recommend MINIMUM kernel 3.13.7 for it also make sure to have at least F2 bios. You might need even newer Kernel for proper GFX support. Tough flashing it basically requires windows but another person that got the dual core version got a newer bios so I dont think thats a problem any more (I got en early batch since I pre-ordered my board). Grub2 had som problems with the F1 bios for me and randomly rebooted after Grub2 started.

But yea thats a 10W SoC (system on a chip), it uses DDR3L and note thy "L". Wont work with normal DDR3 it must be 1.35V DDR3L and SODIMM since thats a requirement by the Bay Trail SoC.
So you can run it of any AC to DC converter for an ITX build. Board it self is just about 10W then ram and what ever else you want is a few watts.

Mine runs at full Turbo of 2.42Ghz during compiling for hours, no throttling so its not running to hot.

its also a very low cost board so.

It do not have HDMI, but it has DVI. No Digital out ithere so its not a perfect HTPC if thats what you want.
There are other models from gigabyte and other manufacturers. This on I linked to is a "legacy" product meaning its meant to replace old systems and interface with older hardware like VGA, COM ports etc. Plus is Dual Gbit lan._________________WS: i7 3930K@4Ghz, 32Gb ram, 256Gb NVME & 128Gb sata SSD, GTX780 3Gb & RX 460 2Gb
NAS: i3 4360 3.7Ghz, 20Gb ram, 256Gb SSD, 36Tb HDD, NIC: Intel 2x1Gbit
ROUTER: J1900 2Ghz, 8Gb ram, 128Gb SSD, NIC: 2x1Gbit, WIFI: Intel AC 7260, Atheros AR5005G

When all you need is video decoding with minimal power consumption I personally would not go for Intel (as it seems VDPAU seems to be better supported and more stable than VAAPI) and I would also think that an A8 or A10 would be pure overkill.
Something like the Sempron 2650 with inbuilt Radeon R3 graphics and a TDP of 25W is much easier to cool and will be powerful enough to decode 1080p video, not to mention that it is considerably cheaper.

The Raspberry Pi can do this.
I also have a 3 year old AMD system with no moving parts but it needs to binary blob driver to render 1080p properly. It seems its no longer on sale.
The Pi also needs a licence to use the Graphics hardware - thats £1.50.

The Pi is much lower cost than the AMD system._________________Regards,

NeddySeagoon

Computer users fall into two groups:-
those that do backups
those that have never had a hard drive fail.

Yeah they are probably overkill, but I'm also running a btrfs mirror set. The Kaveri has AVX support which is useful in RAID I/O. I also run WINE and a Windows VM (libvirt and kvm) to play games on it.